62. Abelardo wants to create several different 7-character names. He want to use arrangements of the first three letters of his name (abe) followed by arrangements of 4 digits in 1984, the year of his birth. How many different screen names can he arrange in this way?
2007-04-22 15:44:22 · 2 answers · asked by stuff 1 in Science & Mathematics ➔ Mathematics
Your explanation is not exactly clear. I assume he wants letter arrangements like aeb or bea, but not aab or eee. The same deal with the numbers.
Since the selection of each is independant of the other, we look at the letters and numbers separately, determine the number of acceptable combinations for each, and multiply them. For the letters, the combinations are 6 (abe, aeb, etc. ) and for the numbers, the combinations are 24. Then there are 144 arrangments of screen names.
2007-04-22 15:50:51 · answer #1 · answered by cattbarf 7 · 0⤊ 0⤋
Is there replacement or not? If there is replacement, there are 3*3*3 = 27 choices for the first three positions and 4*4*4*4=256 choices for the last 4, so with replacement there is 27*256 total choices.
If there is no replacement, then there are 3*2*1 = 6 choices for the first 3 positions and 4*3*2*1 = 24 choices for the last 4 positions. So without replacement there is 6*24 total choices.
2007-04-22 15:51:39 · answer #2 · answered by dodgetruckguy75 7 · 0⤊ 0⤋